Various methods of measurement are used to establish and present estimates of the size of the shadow economy in 76 developing countries, countries with economies in transition and States members of the Organization for Economic Cooperation and Development (OECD). From 1989 to 1993, the average size of the shadow economy as a percentage of gross domestic product (GDP) was 39 per cent in developing countries, 23 per cent in transition countries, and 12 per cent in OECD countries. An increasing burden of taxation and social security contributions combined with rising State regulatory activities are the driving forces behind the growth of the shadow economy. According to some findings, a growing shadow economy has a negative impact on official GDP growth, although other studies show the opposite effect.

Introduction

As crime and other underground economic activities (including the shadow economy) are a fact of life around the world, most societies attempt to control such activities by measures such as punishment, prosecution, economic growth or education. Gathering statistics about who is engaged in underground (or criminal) activities and about the frequency and scale of such activities is crucial for sound decision-making on the allocation of resources in this area. Unfortunately, it is very difficult to get accurate information about underground, or shadow-economy, activities, because those involved are careful to conceal their identities. Estimating shadow-economy activities can therefore be likened to a scientific passion for knowing the unknown.

Although a large literature
2 is devoted to specific aspects of the hidden economy, a comprehensive survey has just been carried out by Schneider and Enste [1]. The subject remains controversial [16], and there are disagreements about the definition of shadow-economy activities, measurement procedures and the use of estimates in economic analysis and addressing policy issues.
3 Nevertheless, around the world, there are strong indications of a growing shadow economy. The size, the causes and the consequences of the shadow economy are different in different countries, but comparisons are possible and they may be of interest to social scientists and the public at large and useful to politicians, who will have to deal with this phenomenon sooner or later. By their very nature, shadow-economy activities are difficult to measure, and there is a wide divergence of opinion among academics, experts in the public sector, policy or economic analysts and politicians, as to what the shadow economy is all about or how big it is.

Nevertheless, the shadow economy is an area of growing concern, and there are several important reasons why politicians and public sector officials should be worried about its size and growth, including the following:

(a) If an increase in the shadow economy is caused mainly by a heavier tax and social security burden, it could lead to an erosion of the tax base and social security contributions, resulting in a decrease in tax revenue and a rising budget deficit, triggering even higher tax rates with a consequent growth in the shadow economy as the cycle continues. A growing shadow economy can therefore be seen as the result of decisions taken by individuals who feel overwhelmed by the demands of the State;

(b) A growing shadow economy implies that economic policy is based on erroneous or unreliable official indicators (such as unemployment rates, labour force statistics and levels of income and consumption). In such a situation, a prospering shadow economy may cause severe difficulties for politicians, because the unreliable official indicators may be used as the basis for questionable policy measures;

(c) On the one hand, a growing shadow economy may provide strong incentives to lure domestic and foreign workers and other resources away from the official economy. On the other hand, two thirds of the income earned in the shadow economy is spent in, and strongly stimulates the growth of, the official economy.
4

The growing concerns referred to above and the complex issues raised by the underground economy inspired the present study, which involved the challenging task of collecting all available data on the shadow economy, in an effort to gain insight into its main causes and its effects on the official economy. The matters covered in the sections below are as follows: first, an attempt is made to define the shadow economy; secondly, empirical results are presented on the size of the shadow economy in 76 countries throughout the world; thirdly, the main causes of the shadow economy are considered; fourthly, the interactions of the official and unofficial economies are analysed; fifthly, the various methods used to estimate the size of the shadow economy are presented; and finally, a summary is provided and various conclusions are drawn.

Definition of shadow economy

Most attempts to measure the shadow economy are hampered by the difficulty of defining the term. According to one commonly used working definition, the shadow economy consists of all currently unregistered economic activities that contribute to the officially calculated (or observed) gross national product (GNP).
5 Smith [24] defines it as "market-based production of goods and services, whether legal or illegal, that escapes detection in the official estimates of gross domestic product". As such definitions leave many open questions, table 1 might shed some light on the content of a possible consensus definition of the legal and illegal underground or shadow economy.

Barter of drugs and stolen goods, smuggling etc.; production or theft of drugs for own use

Involving tax evasion

Involving tax avoidance

Involving tax evasion

Involving tax avoidance

Legal

Unreported income from self-employment; wages, salaries and assets from unreported work related to legal services and goods

Employee discounts and fringe benefits

Barter of legal services and goods

Do-it-yourself work and help given to neighbours

Note: Structure of table based on Lippert and Walker [9], p. 5.

Table 1 shows that the shadow economy includes unreported income from the production of legal goods and services, involving either monetary or barter transactions, hence all economic activities that would generally be taxable were they reported to the State tax authorities. A precise definition of the term seems quite difficult, if not impossible, as "the shadow economy develops all the time according to the 'principle of running water': it adjusts to changes in taxes, to sanctions from the tax authorities and to general moral attitudes, etc." (Mogensen and others [25], p. 5).
6 The subject of tax evasion or tax compliance, already the focus of considerable research [27], is beyond the scope of the present paper.

Size of the shadow economy in 76 countries

For single countries and sometimes for a group of countries, such as the States members of the Organization for Economic Cooperation and Development (OECD) or countries with economies in transition, research has been undertaken to estimate the size of the shadow economy (see Pozo [8], Loayza [7], Lippert and Walker [9], Schneider [13], Lacko [28]) using various methods and different time periods. In tables 2 to 4, an attempt is made to compare estimates of the size of the shadow economy in various countries over a fixed time period, using measurement methods described later in the present paper, in the section entitled "Methods used to estimate the size of the shadow economy",
7 with findings reported on the shadow economy in 76 countries throughout the world for the periods 1989-1990 and 1990-1993.
8

Table 2. Size of the shadow economy in developing countries(Percentage of GDP)

Size of the shadow economy

Developing countries

Physical input (electricity) method (average 1989-1990)

Currency demand approach (average 1989-1990)

MIMICaapproach (average 1990-1993)

Africa

Botswana

27.0

--

--

Egypt

68.0

--

--

Mauritius

20.0

--

--

Morocco

39.0

--

--

Nigeria

76.0

--

--

South Africa

--

9.0
b

--

Tunisia

45.0

--

--

United Republic of Tanzania

--

31.0
c

--

Central and South America

Argentina

--

--

21.8

Bolivia

--

--

65.6

Brazil

29.0

--

37.8

Chile

37.0

--

18.2

Colombia

25.0

--

35.1

Costa Rica

34.0

--

23.2

Ecuador

--

--

31.2

Guatemala

61.0

--

50.4

Honduras

--

--

46.7

Mexico

49.0

33.0
d

27.1 (35.1)
d

Panama

40.0

--

62.1

Paraguay

27.0

--

--

Peru

44.0

--

57.4

Uruguay

35.2

--

--

Venezuela

30.0

--

30.8

Asia

China

Hong Kong
Special Administrative Region

13.0

--

--

Taiwan Province

--

--

16.5
e

Cyprus

21.0

--

India

22.4
f

--

Israel

29.0

--

--

Malaysia

39.0

--

--

Philippines

50.0

--

--

Republic of Korea

38.0

--

20.3
e

Singapore

13.0

--

--

Sri Lanka

40.0

--

--

Thailand

71.0

--

--

Sources: Calculations based on Lacko ([29], table 18) for developing countries in Africa and Asia, and on Loayza [7] for those in Central and South America.
aMultiple-indicator multiple-cause.
bBased on Van der Berg [34], Hartzenburg and Leimann [35], who both used the currency demand approach.
cBased on Bagachwa and Naho ([36], p. 1394), who used the currency demand approach.
dUsing the currency demand approach, Pozo [8] estimates the size of the shadow economy in Mexico, as a percentage of GDP, at 33 per cent in 1989-1990 and 35.1 per cent in 1990-1993.
eEstimated by Yoo and Hyun [37] using the income discrepancy method.
fCalculations based on Bhattacharyya [38].

For Central and South American countries, one estimate is made using the physical input method (Lacko [29]) and one using the MIMIC approach (Loayza [7]). For some countries, such as Brazil, Guatemala and Venezuela, estimates of the size of the shadow economy are quite similar; for others, such as Mexico, Panama and Peru, there are great differences. A ranking of the South American countries using the MIMIC approach shows that the biggest shadow economies, as a percentage of GDP, can be found in Bolivia, at 65.6 per cent of GDP, Panama, at 62.1 per cent, Peru, at 57.4 per cent, and Guatemala, at 50.4 per cent. Ranked lowest are the shadow economies of Costa Rica, at 23.2 per cent of GDP, Argentina, at 21.8 per cent, and Chile, at 18.2 per cent (all estimated for the period 1990-1993). In Asia, the shadow economy of Thailand is the largest, at 71 per cent of GDP, followed by the Philippines, at 50 per cent, and Sri Lanka, at 40 per cent. Hong Kong Special Administrative Region (SAR) of China and Singapore have the smallest shadow economies, each estimated at 13 per cent of GDP. The large size of the shadow economy in some developing countries suggests that it is more a "parallel" or second economy that has not been adequately captured by official statistics.

Transition countries

Table 3. Size of the shadow economy in transition countries(Percentage of GDP)

Average size based on the physical input (electricity) method

Transition countries

1989-1990

1990-1993

1994-1995

States formerly part of the Soviet Uniona

Azerbaijan

21.9

(--)

33.8

(41.0)

59.3

(49.1)

Belarus

15.4

(--)

14.0

(31.7)

19.1

(45.4)

Estonia

19.9

(19.5)

23.9

(35.9)

18.5

(37.0)

Georgia

24.9

(--)

43.6

(50.8)

63.0

(62.1)

Kazakhstan

17.0

(13.0)

22.2

(29.8)

34.2

(38.2)

Kyrgyzstan

--

(13.9)

--

(27.1)

--

(35.7)

Latvia

12.8

(18.4)

24.3

(32.2)

34.8

(43.4)

Lithuania

11.3

(19.0)

26.0

(38.1)

25.2

(47.0)

Republic of Moldava

18.1

(--)

29.1

(--)

37.7

(--)

Russian Federation

14.7

(--)

27.0

(36.9)

41.0

(39.2)

Ukraine

16.3

(--)

28.4

(37.5)

47.3

(53.7)

Uzbekistan

11.4

(13.9)

10.3

(23.3)

8.0

(29.5)

Average for the States formerly part of the Soviet Union

16.7

(16.2)

25.7

(34.9)

35.3

(43.6)

Central and Eastern Europe

Bulgaria

24.0

(26.1)

26.3

(32.7)

32.7

(35.0)

Croatia

22.8
b

(--)

23.5
b

(39.0)

28.5
b

(38.2)

Czech Republic

6.4

(23.0)

13.4

(28.7)

14.5

(23.2)

Hungary

27.5

(25.1)

30.7

(30.9)

28.4

(30.5)

The former Yugoslav Republic of Macedonia

--

(--)

--

(40.4)

--

(46.5)

Poland

17.7

(27.2)

20.3

(31.8)

13.9

(25.9)

Romania

18.0

(20.9)

16.0

(29.0)

18.3

(31.3)

Slovakia

6.9

(23.0)

14.2

(30.6)

10.2

(30.2)

Slovenia

--

(26.8)

--

(28.5)

--

(24.0)

Average for the States of central and eastern Europe

17.6

(17.6)

20.6

(32.4)

20.9

(31.6)

Sources: Calculations based on Johnson and others ([14], table 1, pp. 182-183), Johnson and others ([15], p. 351) and, for data within parentheses, Lacko ([28], table 8).
aFor the States formerly part of the Soviet Union, values calculated for 1990 were used as average values for 1989-1990, since no data for 1990 were available from Johnson and others [14].
bSee Madzarevic and Milkulic ([41], table 9, p. 17), who used the discrepancy method.

The physical input (electricity) method has been applied to the transition countries in central and eastern Europe and to the States that emerged from the breakup of the former Soviet Union. The results, shown in table 3, cover the periods 1989-1990, 1990-1993 and 1994-1995.
9 According to the estimates based on the physical input method applied by Johnson and others [14] (shown together with values based on Lacko [28] for the States that constituted the former Soviet Union, during the period 1990-1993, Georgia had the largest shadow economy, at 43.6 (50.8) per cent of GDP, followed by Azerbaijan, at 33.8 (41) per cent, and the Republic of Moldova, at 29.1 per cent. The Russian Federation was in the middle range, with a shadow economy estimated at 27 (36.9) per cent of GDP. On the basis of Johnson and others, the shadow economies of Belarus, estimated at 14 per cent of GDP, and Uzbekistan, at 10.3 per cent were the smallest. With the sole exception of the estimate for Uzbekistan based on Johnson and others, the shadow economy in all the other States born of the former Soviet Union experienced a strong increase from an average of 25.7 (34.9) per cent based on Lacko) for 1990-1993 to 35.3 (43.6) per cent based on Lacko) for 1994-1995. With regard to the transition countries of central and eastern Europe, the estimates based on Johnson and others for the period 1990-1993 show that Hungary has the largest shadow economy, at 30.7 per cent of GDP, followed by Bulgaria, at 26.3 per cent. The smallest are those of the Czech Republic, at 13.4 per cent of GDP, and Slovakia, at 14.2 per cent. On the basis of the Lacko estimates, the former Yugoslav Republic of Macedonia has the largest shadow economy, at 40.4 per cent of GDP, followed by Croatia, at 39 per cent. The Lacko estimates show that the smallest shadow economies were those of Slovenia, at 28.5 per cent of GDP, and the Czech Republic, at 28.7 per cent. Whereas a strong increase was observed in the shadow economy of States that were part of the former Soviet Union for the periods 1990-1993 and 1994-1995, the average size of the shadow economy in States of central and eastern Europe was almost stable during those periods. The estimates of Johnson and others show that the shadow economy in States of central and eastern Europe averaged 20.6 per cent of GDP (32.4 per cent according to Lacko) over the period 1990-1993 and 20.9 per cent (31.6 per cent according to Lacko) over the period 1994-1995.

Table 4. Size of the shadow economy in OECD countries(Percentage of GDP)

States members of the Organisation for Economic Cooperation and Development

Either the currency demand method or the physical input method was applied to each of the 21 States members of the Organisation for Economic Cooperation and Development (OECD). Two series of figures are based on the currency demand method, one from Schneider [10, 13] and one from Johnson and others [15, 33].
10 The series by Johnson and others, involving estimates of the shadow economy in most OECD countries (20 out of the 21 countries investigated) over the period 1990-1993, shows that the southern European countries had the largest shadow economies as a percentage of GDP: Greece (27.2 per cent), Italy (20.4 per cent), Spain (16.1 per cent) and Portugal (15.6 per cent). A similar result can be found by using estimates from Schneider and, to a much lesser extent, those provided by Lacko [31] through the physical input (electricity) method. Ranked at the lower end by Johnson and others are Switzerland (6.9 per cent), Norway (5.9 per cent) and Austria (5.8 per cent); whereas Schneider finds the United States of America (8.2 per cent), Switzerland (6.9 per cent) and Austria (6.1 per cent) at the bottom. The ranking of the size of the shadow economy in OECD countries by Schneider is supported by other studies.
11

In table 5, OECD averages are shown for 1994-1995 and for 1996-1997. In principle, the ranking of shadow economies by size is similar to that of table 4. However, the size of the shadow economy in all OECD countries has increased compared to the results for 1990-1993. Whereas the average size of the shadow economy in the OECD countries studied was 13.5 per cent of GDP in 1990-1993, it had increased to 16 per cent of GDP in 1994-1995. It increased further to 16.9 per cent in 1996-1997. The findings clearly show that even in the late 1990s the shadow economy was still growing in most OECD countries.

Only a crude comparison can be made of the size of the shadow economy in the various countries and country groupings because, in the studies conducted:

(a) different independent variables (such as tax variables) and different specifications for the dependent variable and the relevant equations were used;
(b) different assumptions about the velocity of currency circulation were made; and
(c) other factors affecting electricity consumption were taken into account. As can be seen from table 6, the average size of the shadow economy in developing countries is by far the largest, at between 35 and 44 per cent of GDP, followed by the transition countries, at between 20.7 per cent and 34.9 per cent, and finally the OECD countries, estimated at 15.1 per cent using the electricity method and at 11.9 per cent using the currency demand method. But such a comparison, as noted above, can only be indicative, since the methods, statistical approaches and specifications used differ widely in the various studies.

Some remarks on the labour force in a shadow economy

After the review given above of the size and growth of the shadow economy in terms of value added over time, the focus on the present section will be on the "shadow labour market", since within the official labour market there is particularly close contact between those who are active in the shadow economy.
12 Moreover, by definition, every shadow economic activity to some extent involves a shadow labour market. Hence, the shadow labour market includes all cases where the employees or employers, or both, occupy a position in the shadow economy. Why do people work in the shadow economy? In the official labour market, the costs that firms (and individuals) have to pay when officially hiring someone are greatly increased by the burden of taxation and social contributions linked to wages, as well as by legal and administrative regulations to control economic activity.
13 In various OECD countries, such costs are greater than the wage effectively earned by the worker, thus providing a strong incentive to work in the shadow economy. The underground use of labour may involve a second job after (or even during) regular working hours. Another form of work in the shadow economy is carried out by individuals who do not participate in the official labour market. A third component consists in the employment of people (for example, clandestine or illegal immigrants) who are not allowed to work in the official economy.

Studying the labour market in the shadow economy is even more difficult than studying value added in the shadow economy, because very little is known about how many hours a shadow economy worker actually works on average (from full time to only a few hours). Empirical facts are therefore not easy to come by. The few estimates available are shown in table 7 for OECD countries.
14 The figures in table 7 give a rough idea of the size of the shadow labour market. For example, the estimates for Denmark show that the population of adult Danes engaged in the shadow economy ranged from 8.3 per cent of the total labour force in 1980 to 15.4 per cent in 1994. In Germany, the figure rose from 8 to 12 per cent during the period 1974-1982, to 22 per cent in 1997-1998.

That is a very strong increase for both countries. The size of the labour force in the shadow economy is also quite large in other countries: in Italy, 30-48 per cent (1997-1998); in Spain, 11.5-32.3 per cent (1997-1998); in Sweden, 19.8 per cent (1997-1998); and in France, 6-12 per cent (1997-1998). In the European Union, at least 10 million people are engaged in shadow-economy activities, and in the OECD countries, about 16 million work on an illicit, irregular or unofficial basis. Those figures demonstrate that the labour market in the shadow economy is thriving, and may explain, for example, why there is such high and persistent unemployment in Germany.

Table 7. Size of the labour force in the shadow economy of selected OECD countries, 1974-1998
(percentage of GDP)

More detailed information on the labour supply in the underground economy is given by Lemieux and others [52] using data from a survey conducted in the city of Quebec, Canada. In particular, their study provides some economic insight into the size of the distortion caused by income taxes and the welfare system. The findings of the study suggest that hours worked in the shadow economy are responsive to changes in net wages in the regular (official) sector. The study also provides some support for the existence of a Laffer curve. The Laffer curve suggests that an increase in the marginal tax rate leads to a decrease in tax revenue when the tax rate is too high. According to the empirical findings of the study, that is attributable to a misallocation of work from the official to the informal sector, where it is not taxed. In that case, the exchange of labour market activities between the two sectors is high. The empirical findings clearly indicate that "participation rates and hours worked in the underground sector also tend to be inversely related to the number of hours worked in the regular sector" (Lemieux and others, [52], p. 235). The findings demonstrate a large negative elasticity of hours worked in the shadow economy with respect to the wage rate in the regular sector and also a high mobility between the sectors.

Main causes of the growth of the shadow economy

Increase in the burden of taxation and social security contributions

In almost all studies,
15 it has been found that an increase in taxes and social security contributions is one of the main causes of the growth of the shadow economy. Since taxes affect choices of labour and leisure and also stimulate the labour supply in the shadow economy, or the untaxed sector of the economy, the distortion of that choice is a major concern of economists. The bigger the difference between the total cost of labour in the official economy and the after-tax earnings from work, the greater is the incentive to avoid the loss by working in the shadow economy. Since the difference depends broadly on the social security system and the overall tax burden, they are key features of the existence and growth of the shadow economy. But even tax reforms with major deductions in the tax rate deductions will not lead to a substantial decrease in the size of the shadow economy. They will only be able to stabilize the size of the shadow economy and avoid a further increase. Social networks and personal relationships, the high profit from irregular activities and associated investments in real and human capital are strong ties that prevent people from transferring to the official economy. For Canada, Spiro [54] expected similar reactions of people facing an increase in indirect taxes (value added tax (VAT) and goods and services tax (GST)). After the introduction of GST in 1991, in the midst of a recession, people suffering economic hardship because of the recession turned to the shadow economy, which led to a substantial loss in tax revenue. "Unfortunately, once this habit is developed, it is unlikely that it will be abandoned merely because economic growth resumes." (Spiro [54], p. 255). They may not return to the formal sector, even in the long run. That makes it even more difficult for politicians to carry out major reforms, because they may not gain much from them.
16

The most important factor in neoclassical models is the marginal tax rate. The higher the marginal tax rate, the greater is the substitution effect and the bigger the distortion of the decision between labour and leisure. Especially when taking into account that the individual can also receive income in the shadow economy, the substitution effect is definitely larger than the income effect
17 and, hence, the individual works less in the official sector. The overall efficiency of the economy is therefore, ceteris paribus, lower, and the distortion leads to a welfare loss (based on official GNP and taxation). But the welfare might also be viewed as increasing, if the welfare of those who are working in the shadow economy were taken into account, too (Thomas [6], pp. 134-137).

Empirical results of the influence of the tax burden on the shadow economy are provided in the studies of Schneider [11, 53] and Johnson and others [15, 33]. They all found strong evidence for the general influence of taxation on the shadow economy. This strong influence of indirect and direct taxation on the shadow economy will be further demonstrated by showing empirical results for Austria and the Scandinavian countries. In the case of Austria, Schneider [11] estimates a currency demand function including as driving forces for the shadow economy the following four types of variables:

(a) The burden of total direct taxation;

(b) The burden of indirect taxation;

(c) The complexity of the tax system;

(d) The intensity of government regulation.

The results of the application of the currency demand function are shown in table 8.

All coefficients of the independent variables have the theoretically expected sign and, with the exception of the indirect tax burden, are statistically significant at the 95 per cent confidence level. The other test statistics show satisfactory results, In particular, the "true ex-post" forecast of currency demand for the period 1985-1991 indicates that the major independent factors in the currency demand function are included. The driving force for the shadow economy activities is the direct tax burden (including social security payments), which has the biggest impact, followed by the intensity of regulation and the complexity of the tax system. A similar result has been achieved by Schneider [26] for Scandinavian countries (Denmark, Norway and Sweden). In all three countries, various tax variables (average direct tax rate and average total tax rate (consisting of indirect and direct tax rates)) and marginal tax rates have the expected positive sign (on currency demand) and are highly significant statistically. Similar results were reached by Kirchgaessner [55, 56] for Germany and by Kloveland [57] for Norway and Sweden.

Table 8. Results of the application of the currency demand function to Austria

Dependent variable: real currency

Independent variables

per capita, ln (CURt/POPt)
1956-1991

estimation period,
1956-1985

Lagged dependent variable

0.534**

0.551**

ln (
CURt-1/POPt-1)

(8.91)

(9.43)

Real consumption per capita

0.703**

0.724**

ln (
Ct/POPt)

(5.49)

(5.99)

Number of Eurocheque systems per capita

-0.213*

-0.174*

ln (
ESt-1/POPt-1)

(-2.51)

(-2.09)

Real interest rate on bonds

-0.123**

-0.139*

ln (
IRt)

(-2.51)

(-2.65)

Direct tax burden (including social security payments)

0.173**

0.182*

ln (
DIRTt)

(3.09)

(2.86)

Indirect tax burden

0.117(*)

0.123(*)

ln (
INDTt)

(1.88)

(1.92)

Complexity of the tax system

0.154**

0.147**

ln (
VISTt)

(2.77)

(2.86)

Intensity of regulation

0.166**

0.159**

ln (
REGt)

(2.94)

(2.72)

Constant term

-2.24(*)

-2.39(*)

(-1.80)

(-1.74)

Test statistics

Rβ

0.992

0.990

S.E

0.014

0.015

Durbin's h

1.06

1.16

rho (1)

0.18

0.20

D.F.

27

21

Ex-post Forecast

RMSE

-

1.51

Theil's U 1

-

0.42

Note: All equations are estimated by an ordinary least-squares procedure using annual data. Rβ is the coefficient of determination (corrected for the degrees of freedom); S.E. shows the standard error of the estimation. Durbin's h is Durbin's h-test against auto-correlation when lagged dependent variables are used as regressors. Rho (1) is the auto-correlation coefficient of first order. D.F. stands for the "degrees of freedom". RMSE is the root mean squared error and Theil's U 1 stands for Theil's inequality coefficient. The term "ln" indicates that these variables have been transformed to natural logarithms. Numbers in parentheses below coefficient estimates are t-values. (*),* and** indicate significance at the 90, 95 and 99 per cent confidence level, respectively.

Several other recent studies provide further evidence of the influence of income tax rates on the shadow economy. Cebula [58], using Feige data for the shadow economy, found evidence of the impact of government income tax rates, Internal Revenue Service (IRS) audit probabilities and IRS penalty policies on the relative size of the shadow economy in the United States. Cebula concludes that refraining from any further increase of the top marginal income tax rate may at least curb a further increase in the shadow economy, while increased IRS audits and penalties might reduce the size of the shadow economy. His findings indicate that there is generally a strong influence of State activities on the size of the shadow economy. For example, if the marginal federal personal income tax rate increases by one percentage point, ceteris paribus, the shadow economy rises by 1.4 percentage points. In another investigation, Hill and Kabir [59] found empirical evidence that marginal tax rates are more relevant than average tax rates, and that a substitution of direct taxes by indirect taxes seems unlikely to improve tax compliance. Further evidence of the effects of taxation on the shadow economy is presented by Johnson and others [33], who come to the conclusion that it is not higher tax rates per se that increase the size of the shadow economy, but the ineffective and discretionary application of the tax system and government regulations. Their finding that there is a negative correlation
18 between the size of the unofficial economy and the top (marginal) tax rates might be unexpected. But since other factors like tax deductibility, tax relief, tax exemptions, the choice between different tax systems and various other options for legal tax avoidance were not taken into account, it is no great surprise.
19 On the other side, Johnson and others [33] find a positive correlation between the size of the shadow economy and the corporate tax burden. They come to the overall conclusion that there is a large difference between the impact of either direct taxes or the corporate tax burden. Institutional aspects, like the efficiency of the administration, the extent of control rights held by politicians and bureaucrats, and the amount of bribery and especially corruption, therefore play a major role in the bargaining game between the Government and the taxpayers.

Intensity of regulations

The increase of the intensity of regulation (often measured by the number of laws and regulations, such as licence requirements) is another important factor that reduces the freedom of choice for individuals engaged in the official economy.
20 Labour market regulations, trade barriers and labour restrictions for foreigners are relevant examples. Johnson and others [33] find overall significant empirical evidence of the influence of (labour) regulations on the shadow economy, and the impact is clearly described and theoretically derived in other studies, for example, the study on Germany carried out by the Deregulation Commission in 1990-1991. Regulations lead to a substantial increase in labour costs in the official economy. But since most of the costs can be shifted on to the employees, they provide another incentive to work in the shadow economy, where they can be avoided. Empirical evidence supporting the model of Johnson and others [14], which predicts, inter alia, that countries with more general regulation of their economies tend to have a higher share of the unofficial economy in total GDP, is found in their empirical analysis. A one-point increase of the regulation index (ranging from 1 to 5, with 5 corresponding to the most regulation in a country), ceteris paribus, is associated with an 8.1 percentage point increase in the share of the shadow economy, when controlled for GDP per capita (Johnson and others [33], p. 18). They conclude that it is the enforcement of regulations, which is the key factor in the burden levied on firms and individuals, and not the overall extent of regulations, mostly not enforced, that drives firms into the shadow economy. Friedman and others [60] reach a similar result. In their study, every available measure of regulation is significantly correlated with the share of the unofficial economy and the sign of the relationship is unambiguous: more regulation is correlated with a larger shadow economy. A one-point increase in an index of regulation (ranging from 1 to 5) is associated with a 10 per cent increase in the shadow economy for 76 developing countries, transition countries and developed countries.

The above-mentioned findings demonstrate that Governments should put more emphasis on improving enforcement of laws and regulations, rather than increasing their number. Some Governments, however, prefer this policy option (more regulations and laws) when trying to reduce the shadow economy, mostly because it leads to an increase in power of the bureaucrats and to a higher rate of employment in the public sector.
21

Social transfers

The social welfare system leads to strong negative incentives for beneficiaries to work in the official economy since their marginal tax rate often equals or nearly reaches 100 per cent. That can be derived either from the neoclassical leisure-income model or from empirical results.
22 Such a system provides major disincentives for individuals who are getting welfare payments to even search for work in the official economy, since their overall income is much higher when they are still receiving the transfers, while possibly working in the underground economy.

Public sector services

An increase in the size of the shadow economy leads to reduced State revenues, which in turn reduces the quality and quantity of publicly provided goods and services. Ultimately, this can lead to an increase in the tax rates for firms and individuals in the official sector, quite often combined with a deterioration in the quality of the public goods (such as the public infrastructure) and of the administration, with the consequence of even stronger incentives to participate in the shadow economy. Johnson and others [33] present a simple model of this relationship. Their findings show that smaller shadow economies appear in countries with higher tax revenues, if achieved by lower tax rates, fewer laws and regulations and less bribery facing enterprises. Countries with a better rule of the law that is financed by tax revenues also have smaller shadow economies. Transition countries have higher levels of regulation leading to a significantly higher incidence of bribery, higher effective taxes on official activities and a large discretionary framework of regulations, and consequently to a higher shadow economy. The overall conclusion is that "wealthier countries of the OECD, as well as some in eastern Europe, find themselves in the 'good equilibrium' of relatively low tax and regulatory burden, sizeable revenue mobilization, good rule of law and corruption control, and [relatively] small unofficial economy. By contrast, a number of countries in Latin America and the former Soviet Union exhibit characteristics consistent with a 'bad equilibrium': tax and regulatory discretion and burden on the firm is high, the rule of law is weak, and there is a high incidence of bribery and a relatively high share of activities in the unofficial economy" ([15], p. 388).

Effects of the shadow economy on the official economy

In order to study the effects of the shadow economy on the official economy, several studies integrate underground economies into macroeconomic models.
23 Houston [65] develops a theoretical macroeconomic model of the business cycle as well as tax and monetary policy linkages with the shadow economy. He concludes from his investigation of the growth of the shadow economy that, on the one hand, its effect should be taken into account in setting tax and regulatory policies, and, on the other, the existence of a shadow economy could lead to an overstatement of the inflationary effects of fiscal or monetary stimuli. Adam and Ginsburgh [66] focus on the implications of the shadow economy on official growth in their study for Belgium. They find a positive relationship between the growth of the shadow economy and the official one, and under certain assumptions (that is, very low costs of entry into the shadow economy due to a low probability of enforcement), they conclude that an expansionary fiscal policy has a positive stimulus for both the formal and informal economies. A study for the United States by Fichtenbaum [67] argues that the United States productivity slowdown over the period 1970 to 1989 was vastly overstated, as the underreporting of income due to the more rapid growth of the United States shadow economy during that period was not taken into account.
24

Another hypothesis is that a substantial reduction of the shadow economy leads to a significant increase in tax revenues, and therefore to a greater quantity and quality of public goods and services, which ultimately can stimulate economic growth. Some authors found evidence for that hypothesis. A recent study by Loayza [7] presents a simple macroeconomic endogenous growth model whose production technology depends on congestable public services. The determinants and effects of the informal sector are studied, where excessive taxes and regulations are imposed by Governments and where the capability to enforce compliance is low. The model leads to the conclusion that in economies where the statutory tax burden is larger than the optimal tax burden, and where the enforcement of compliance is too weak, the increase in the relative size of the informal economy generates a reduction of economic growth. The linkage is due to the strongly negative correlation between the informal sector and public infrastructure indices, with public infrastructure being the key element for economic growth. For example, Loayza finds empirical evidence that, in Latin American countries, if the shadow economy increases by one percentage point of GDP, ceteris paribus, the growth rate of official real GDP per capita decreases by 1.22 percentage points. This negative impact of informal sector activities on economic growth is not broadly accepted.
25 For example, the key feature of the model has been criticized, because the model is based on the assumption that the production technology essentially depends on tax-financed public services, which are subject to congestion. In addition, the informal sector is not paying any taxes, but must pay penalties that are not used to finance public services. The negative correlation between the size of the informal sector and economic growth is therefore not very surprising.

Depending on the prevailing view of the informal sector, the opposite conclusion might be reached. In the neoclassical view, the underground economy is optimal in the sense that it responds to the demand of the economic environment for urban services and small-scale manufacturing. From this point of view, the informal sector provides the economy with a dynamic and entrepreneurial spirit and can lead to more competition, higher efficiency and strong boundaries and limits for government activities. The informal sector may offer great contributions "to the creation of markets, increase financial resources, enhance entrepreneurship, and transform the legal, social, and economic institutions necessary for accumulation" (Asea [72],

p. 166). The voluntary self-selection between the formal and informal sectors, as described above in microeconomic models, may provide a higher potential for economic growth and, hence, a positive correlation between an increase in the informal sector and economic growth. The effects of an increase in the size of the shadow economy on economic growth therefore remain highly ambiguous.

The empirical evidence of the hypotheses is also not clear. On the one hand, since many Latin American countries had or still have a tradition of excessive regulations and weak government institutions, Loayza [7] finds some evidence of the implications of his growth model during the early 1990s in those countries. The increase in the size of the shadow economy negatively affects official GDP growth by reducing the availability of public services for everyone in the economy, and by causing the existing public services to be used less efficiently, or not at all. On the other hand, the positive effects of shadow economy activities should also be considered. Empirical findings of Schneider [21] show clearly that over 66 per cent of the earnings in the shadow economy are immediately spent in the official sector. The positive effects of this expenditure for economic growth and for the indirect tax revenues must be taken into account as well. Bhattacharyya [38] found clear evidence that, in the United Kingdom (1960-1984), the hidden economy had a significant positive effect on consumer expenditures in the official economy. He points out that the hidden economy has a positive effect on consumer expenditure for non-durable goods and services, and an even stronger positive effect on consumer expenditure for durable goods and services.
26

Methods used to estimate the size of the shadow economy

As has already been mentioned above in the section on the definition of the shadow economy, the attempt to measure the size of a shadow economy is a difficult and challenging task. In the present section, a comprehensive overview is given of the current knowledge of the various procedures for estimating the size of the shadow economy. To measure the size and development of the shadow economy, three different types of methods are most widely used.
27 They are briefly discussed in the next three sections.

Direct approaches

There are micro-approaches that employ either well-designed surveys and samples based on voluntary replies or tax auditing and other compliance methods. Sample surveys designed for estimating the size of the shadow economy are widely used in a number of countries.
28 The main disadvantage of such a method is that it presents the flaws of all surveys: the precision of averages and results depend greatly on the willingness of respondents to cooperate. It is difficult to assess the rise of undeclared work from a direct questionnaire. Most interviewees hesitate to confess fraudulent behaviour and responses are seldom reliable, so that it is difficult to calculate a true estimate, in monetary terms, of the amount of undeclared work. The main advantage of the method lies in the detailed information that it provides about the structure of the shadow economy, but the results from such surveys are highly sensitive to the way in which the questionnaire is formulated.
29

Estimates of the shadow economy can also be based on the discrepancy between income declared for tax purposes and that measured by selective checks. Fiscal auditing programmes have been particularly effective in that regard. Designed to measure the amount of undeclared taxable income, they have been used to calculate the size of the shadow economy in several countries.
30 A number of difficulties beset this approach. First, using tax compliance data is equivalent to using a possibly biased sample of the population. However, since a selection of taxpayers for auditing is generally not random, but based on properties of submitted tax returns that indicate a certain likelihood of fraud, such a sample is not a random one of the whole population. That factor is likely to bias compliance-based estimates of the shadow economy. Secondly, estimates based on tax audits reflect the portion of shadow economy income that the authorities succeeded in discovering, and are likely to be only a fraction of hidden income.

A further disadvantage of the two direct methods (surveys and tax auditing) is that they lead to only point estimates. Moreover, since it is unlikely that they capture all shadow economy activities, they can be seen as providing estimates at the lower end of the scale. They are currently unable to provide estimates of the development and growth of the shadow economy over a longer period of time. As already noted, however, they have at least one considerable advantage: they can provide detailed information about the structure of shadow economy activities and about those who work in the shadow economy.

Indirect approaches

Indirect approaches, which are also called "indicator" approaches, are mostly macroeconomic measures that use various economic and other indicators containing information about the development of the shadow economy over time. Currently, there are five indicators that leave some traces of the development of the shadow economy, as described below.

Discrepancy between national expenditure and income statistics

One approach is based on discrepancies between income and expenditure statistics. In national accounting, the income measure of GNP should be equal to the expenditure measure of GNP. Thus, if an independent estimate of the expenditure site of the national accounts is available, the gap between the expenditure measure and the income measure can be used as an indicator of the scale of the shadow economy.
31 However, since national accounts statisticians will be anxious to minimize this discrepancy, the initial discrepancy or first estimate, rather than the published discrepancy, should be employed for this purpose. If all the components of the expenditure site were measured without error, then this approach would indeed yield a good estimate of the scale of the shadow economy. Unfortunately, that is not the case, and the discrepancy therefore reflects all omissions and errors everywhere in the national accounts statistics as well as the shadow economy activity. The estimates may therefore be very crude and of questionable reliability.
32

The discrepancy between the official and actual labour force

A decline in the participation of the labour force in the official economy can be seen as an indication of increased activity in the shadow economy. If the participation of the total labour force is assumed to be constant, a decreasing official rate of participation can be seen as an indicator of an increase in the activities of the shadow economy, ceteris paribus.
33 The weakness of this method is that differences in the rate of participation may also have other causes. Moreover, people can work in the shadow economy and have a job in the official economy. Such estimates may therefore be viewed as weak indicators of the size and development of the shadow economy.

Transactions approach

This approach has been developed by Feige.
34 It assumes that there is a constant relation over time between the volume of transactions and official GNP. Feige's approach therefore starts from Fisher's quantity equation,

Assumptions have to be made about the velocity of money and about the relationships between the value of total transactions (p*T) and total (official + unofficial) nominal GNP. Relating total nominal GNP to total transactions, the GNP of the shadow economy can be calculated by subtracting the official GNP from total nominal GNP. However, to derive figures for the shadow economy, Feige has to assume a base year in which there is no shadow economy. Therefore, the ratio of p*T to total nominal (official = total) GNP was "normal" and would have been constant over time, if there had been no shadow economy. This method, too, has several weaknesses, for instance, the assumption of a base year with no shadow economy and the assumption of a normal ratio of transactions constant over time. Moreover, to obtain reliable estimates of the shadow economy, precise figures of the total volume of transactions should be available. This availability might be especially difficult to achieve for cash transactions, because they depend, among other factors, on the durability of bank notes, in terms of the quality of the paper on which they are printed.
35 Also, in this approach, the assumption is made that all variations in the ratio between the total value of the transactions and the officially measured GNP are due to the shadow economy. This means that a considerable amount of data is required in order to eliminate financial transactions from "pure" cross payments, which are totally legal and have nothing to do with the shadow economy. In general, although this approach is theoretically attractive, the empirical requirements necessary to obtain reliable estimates are so difficult to fulfil that its application may lead to doubtful results.

Currency demand approach

The currency demand approach was first used by Cagan [96], who calculated a correlation of the currency demand and the tax pressure (as one cause of the shadow economy) for the United States over the period 1919 to 1955. Twenty years later, Gutmann [97] used the same approach, but did not use any statistical procedures. Instead, he only looked at the ratio between currency and demand deposits over the years 1937 to 1976.

Cagan's approach was further developed by Tanzi [98, 99], who econometrically estimated a currency demand function for the United States for the period 1929 to 1980 in order to calculate the shadow economy. His approach assumes that shadow (or hidden) transactions are undertaken in the form of cash payments, so as to leave no observable traces for the authorities. An increase in the size of the shadow economy will therefore increase the demand for currency. To isolate the resulting excess demand for currency, an equation for currency demand is econometrically estimated over time. All possible conventional factors, such as the development of income, payment habits and interest rates, are subject to control.

Additionally, such variables as the direct and indirect tax burden, government regulations and the complexity of the tax system, which are assumed to be the major factors causing people to work in the shadow economy, are included in the estimation equation. The basic regression equation for the currency demand, proposed by Tanzi [99], is the following:

The excess increase in currency, which is the amount unexplained by the conventional or normal factors (mentioned above) is then attributed to the rising tax burden and the other reasons leading people to work in the shadow economy. Figures for the size and development of the shadow economy can be calculated in a first step by comparing the difference between the development of currency when the direct and indirect tax burden (and government regulations) are held at its lowest value, and the development of currency with the current (much higher) burden of taxation and government regulations. Assuming in a second step the same income velocity for currency used in the shadow economy as for legal M1 in the official economy, the size of the shadow economy can be computed and compared to the official GDP.

The currency demand approach is one of the most commonly used approaches. It has been applied to many OECD countries [12, 13, 15, 40], but has nevertheless been criticized on various grounds [6, 8, 18, 86, 95]. The most commonly raised objections to this method are as follows:

(a) Not all transactions in the shadow economy are paid in cash. Isachsen and Strom
37 used the survey method to find out that in Norway, in 1980, roughly 80 per cent of all transactions in the hidden sector were paid in cash. The size of the total shadow economy
(including barter
) may thus be even larger than previously estimated;

(b) Most studies consider only one particular factor, the tax burden, as a cause of the shadow economy. But other factors, such as the impact of regulations, taxpayers' attitudes toward the State and tax morality, are not considered, because reliable data for most countries are not available. If, as seems likely, these other factors also have an impact on the extent of the hidden economy, it might again be higher than reported in most studies;
38

(c) A further weakness of this approach, at least when applied to the United States, is discussed by Garcia [101], Park [86] and Feige [91], who point out that increases in currency demand deposits are due largely to a slowdown in demand deposits rather than to an increase in currency caused by activities in the shadow economy;

(d) Blades [102] and Feige [80, 103] criticize Tanzi's studies on the grounds that the United States dollar is used as an international currency. Tanzi should

have considered allowed United States dollars, which are used as an international currency and held in cash abroad.
39 Moreover, Frey and Pommerehne [4]

and Thomas [6, 18 and 95] claim that Tanzi's parameter estimates are not very stable;
40

(e) Another weak point of this procedure, in most studies, is the assumption of the same velocity of money in both types of economy. As Hill and Kabir [59] for Canada and Kloveland [57] for the Scandinavian countries argue, there is already considerable uncertainty about the velocity of money in the official economy; the velocity of money in the hidden sector is even more difficult to estimate. Without knowledge about the velocity of currency in the shadow economy, assumption of an equal money velocity in both sectors has to be accepted;

(f) Finally, the assumption of no shadow economy in a base year is open to criticism. Relaxing this assumption would again imply an upward adjustment of the figures attained in the bulk of the studies already undertaken.

Physical input (electricity consumption) method

To measure overall (official and unofficial) economic activity in an economy, Kaufmann and Kaliberda [107] assume that the consumption of electric power is the single best physical indicator of overall economic activity. Overall (official and unofficial) economic activity and electricity consumption have been empirically observed throughout the world to move in lockstep with an electricity/GDP elasticity usually close to one. By having a proxy measurement for the overall economy and subtracting it from estimates of official GDP, Kaufmann and Kaliberda derive an estimate of unofficial GDP. Kaufmann and Kaliberda thus suggest that the growth of total electricity consumption is an indicator for representing growth of official and unofficial GDP. According to this approach, the difference between the gross rate of registered (official) GDP and the gross rate of total electricity consumption can be attributed to the growth of the shadow economy. This method is very simple and appealing; however, it can also be criticized on the following grounds:

(a) Not all shadow economy activities
(such as personal services
) require a considerable amount of electricity. Other energy sources can be used
(gas, oil, coal etc.
), so that only a part of the shadow economy will be captured;

(b) Over time, there has been considerable technical progress. Both the production and use of electricity are more efficient than in the past, and that will apply in both official and unofficial uses;

(c) There may be considerable differences or changes in the elasticity of electricity/GDP across countries and over time.
42

Lacko method

Lacko [28, 29, 108] assumes that a certain part of the shadow economy is associated with the household consumption of electricity. It includes, inter alia, so-called household production, do-it-yourself activities and other non-registered production and services. Lacko assumes that in countries where the section of the shadow economy associated with household electricity consumption is high, the rest of the hidden economy, that is, the part that Lacko cannot measure, will also be high. Lacko ([29], pp. 19 ff.) assumes that in each country a part of the household consumption of electricity is used in the shadow economy.

Lacko's approach ([108], p.133) can be described by the following two equations:

where

i is the number assigned to the country,

E
i is per capita household electricity consumption in country i in millions of tons,

C
i is per capita real consumption of households without the consumption of electricity in country i in United States dollars (at purchasing power parity),

PR
i is the real price of consumption of 1 kilowatt-hour of residential electricity in United States dollars (at purchasing power parity),

G
i is the relative frequency of months when heating is needed in homes in country i,

Q
i is the ratio of energy sources other than electric energy to all energy sources in household energy consumption,

H
i is the per capita output of the hidden economy,

T
i is the ratio of the sum of paid personal income, corporate profit and taxes on goods and services to GDP,

S
i is the ratio of public social welfare expenditures to GDP,

and D
i is the sum of number of dependants over 14 years and of inactive earners, both per 100 active earners.

In a cross-country study, Lacko econometrically estimates equation (1), substituting equation (2) for H
i. The econometric estimation results can then be used to establish an ordering of the countries with respect to electricity use in their shadow economies. For the calculation of the actual size (value added) of the shadow economy, Lacko should know how much GDP is produced by one unit of electricity in the shadow economy of each country. Since the data are not known, Lacko takes the results obtained from shadow economy estimations carried out for a market economy using another approach during the early 1990s, and applies the results to the other countries. Lacko used the shadow economy of the United States as such a base (the shadow economy value of 10.5 per cent of GDP taken from Morris [109]), and then calculated the size of the shadow economy for other countries. lacko's method is also open to the following criticism:

(a) Not all shadow economy activities require a considerable amount of electricity and other energy sources can be used;

(b) Shadow economy activities do not take place only in the household sector;

(c) It is doubtful whether the ratio of social welfare expenditures can be used as the explanatory factor for the shadow economy, especially in transition countries and developing countries;

(d) It is not clear which base value of the shadow economy is the most reliable in calculating the size of the shadow economy for all other countries, especially the transition countries and developing countries.

All methods described so far that are designed to estimate the size and development of the shadow economy consider just one indicator that must capture all effects of the shadow economy. However, it is obvious that its effects show up simultaneously in the production, labour and money markets. An even more important critique is that the causes that determine the size of the hidden economy are taken into account only in some of the monetary approach studies that usually consider one cause, the burden of taxation. The model approach explicitly considers multiple causes leading to the existence and growth of the shadow economy over time, with the multiple effects that it entails. The empirical method used is quite different from those used so far. It is based on the statistical theory of unobserved variables, which considers multiple causes and multiple indicators of the phenomenon to be measured. For the estimation, a factor-analytic approach is used to measure the hidden economy as an unobserved variable over time. The unknown coefficients are estimated in a set of structural equations within which the unobserved variable cannot be measured directly. The DYMIMIC (dynamic multiple-indicators multiple-causes) model consists in general of two parts, while the measurement model links the unobserved variables to observed indicators. The structural equations model specifies causal relationships among the unobserved variables. In this case, there is one unobserved variable, the size of the shadow economy. It is assumed to be influenced by a set of indicators for the size of the shadow economy, thus capturing the structural dependence of the shadow economy on variables that may be useful in predicting its movement and size in the future. The interaction over time between the causes Z
it (i = 1, 2, ..., k), the size of the shadow economy X
t and the indicators Y
jt (j = 1, 2, ..., p) is shown in figure I.

Figure I. Development of the shadow economy over time

There is a large body of literature [6, 8, 10, 12, 15, 19, 20, 33] on the possible causes and indicators of the shadow economy. Causes of the following three types have been identified:

(a) The burden of direct and indirect taxation, both actual and perceived. A rising burden of taxation provides a strong incentive to work in the shadow economy;

(b) The burden of regulation as a proxy for all other State activities. It is assumed that increases in the burden of regulation give a strong incentive to enter the shadow economy;

(c) The tax morality (citizens' attitudes towards the State), which describes the readiness of individuals (at least partly) to leave their official occupations and enter the shadow economy. It is assumed that a declining tax morality tends to increase the size of the shadow economy.
44

A change in the size of the shadow economy may be reflected in the following indicators:

(a) Development of monetary indicators. If activities in the shadow economy rise, additional monetary transactions are required;

(b) Development of the labour market. Increasing participation of workers in the hidden sector results in a decrease in participation in the official economy. Similarly, increased activities in the hidden sector may be expected to be reflected in shorter working hours in the official economy;

(c) Development of the production market. An increase in the shadow economy means that inputs
(especially labour
) move out of the official economy
(at least partly
). Such displacement might have a depressing effect on the official growth rate of the economy.

The latest use of the model approach has been undertaken by Giles [19, 20] and by Giles, Linsey and Gupsa [116]. They basically estimate a comprehensive (dynamic) MIMIC model to get a time-series index of the hidden/measured output of New Zealand or Canada, and then estimate a separate cash-demand model to obtain a benchmark for converting this index into percentage units. Unlike earlier empirical studies of the hidden economy, they paid proper attention to the non-stationary, and possible co-integration of time-series data in both models. This MIMIC model treats hidden output as a latent variable, and uses several (measurable) causal variables and indicator variables. The former include measures of the average and marginal tax rates, inflation, real income and the degree of regulation in the economy. The latter include changes in the (male) labour force participation rate and in the cash/money supply ratio. In their cash-demand equation they allow for different velocities of currency circulation in the hidden and recorded economies. Their cash-demand equation is not used as an input to determine the variation in the hidden economy over time. It is used only to obtain the long-run average value of hidden/measured output, so that the index for this ratio predicted by the MIMIC model can be used to calculate a level and the percentage units of the shadow economy. The latest combination by Giles of the currency demand method and the MIMIC approach clearly shows that some progress in the technique used in estimating the shadow economy has been achieved and a number of critical difficulties have been overcome.

Comparison of the results of the estimation of the shadow economy using different methods

As discussed above, there are nine different methods used to estimate the shadow economy. Table 9 shows the empirical results of the application of those methods to Canada, Germany, Italy, the United Kingdom and the United States.

Table 9
(Click on the table to enlarge)

The survey method used for all five countries provides lower estimates ranging from 1.5 per cent to 4.5 per cent for the period 1970-1980. The tax auditing method provides higher estimates of the shadow economy ranging from 2.9 per cent to 8.2 per cent for the period 1970-1980. Both methods also show that the shadow economy increases over time (for example, in the United States). The two discrepancy methods (expenditure versus income and official versus actual labour force) show no clear pattern. For some countries, they produce high shadow economy values (compared to the other methods used, as in the case of Germany); for some, the values are low (as in the case of Canada). Nor do they show a consistent time pattern. The physical input (electricity) method, for which only values for the period 1986-1990 are available for all five countries, shows values in the middle range for all countries (average value of 12.7 per cent over all countries and all periods). A comparison of the three monetary approaches (currency demand, cash-deposit ratio and transactions approach) reveals a clear pattern. The largest shadow economies for all five countries were achieved using the transactions approach (Feige method), ranging from 15 per cent to 35 per cent of GNP (average value of 21.9 per cent over all countries and periods). Somewhat lower results were achieved using the cash-deposit ratio approach (Gutmann method), ranging between 10 per cent and 30 per cent for all countries (average value of 15.5 per cent over all countries and all periods). Considerably lower values were achieved using the currency demand approach, ranging from 4 per cent to 20 per cent of GNP over the period 1970-1990 for all five countries (average value of 8.9 per cent over all countries and periods). The currency demand approach shows a strongly rising shadow economy in all five countries, a result opposite to that given by the transactions and cash-deposit methods. The model approach shows values in the medium range, from 6.1 to 10.5 per cent for the period 1976-1980 (average value of 7.9 per cent for all countries over all periods). In general, these results demonstrate quite clearly that a huge range of estimates of the shadow economy for a country in a given time span is achievable using different calculation methods. Hence, there is a need for great caution when interpreting the size of the shadow economy of a country using only one method.

Summary and conclusions

There are many obstacles to be overcome to measure the size of the shadow economy and to analyse its impact on the official economy, although some progress has been made. The present paper has shown that while it is difficult to estimate the size of the shadow economy, it is not impossible. It has been demonstrated that with various methods, such as the currency demand method, the physical input method and the model approach, some insights can be provided into the size and development of the shadow economy of developing countries, transition countries and OECD countries. The results achieved through the use of these methods give the general impression that, in all the countries investigated, the shadow economy has become remarkably large.

In summary, there appears to be no best or commonly accepted method; each approach has its specific strengths and weaknesses as well as specific insights and results. Although the different methods provide a rather wide range of estimates, there is a common finding that the size of the shadow economy has been growing over the recent decade in most transition countries and in all the OECD countries studied. A similar finding has emerged for the shadow labour market, which is attracting growing attention because of high unemployment in European OECD countries. Furthermore, the results of the present survey show that an increasing burden of taxation and social security payments, combined with rising State regulatory activities, is the major driving force for the growth of the shadow economy. According to some studies, a growing shadow economy has a negative impact on official GDP growth, but other studies show a positive impact, hence, much more research is needed. Finally, shadow economies are a complex phenomenon, present to an important extent even in industrialized and developed economies. People engage in shadow economic activity for a variety of reasons, the most important of which include government actions, in particular, taxation and regulatory measures. With those two insights goes a third and no less important one: a Government that wants to decrease shadow economic activity has to first and foremost analyse the complex and frequently contradictory implications of its own policy decisions.

Norman V. Loayza, "The economics of the informal sector: a simple model and some empirical evidence from Latin America",
Carnegie-Rochester Conference Series on Public Policy, vol. 45 (1996), pp. 129-162.

Owen Lippert and Michael Walker, eds.,
The Underground Economy: Global Evidence of its Size and Impact (Vancouver, British Columbia, The Fraser Institute, 1997).

Friedrich Schneider, "Measuring the size and development of the shadow economy. Can the causes be found and the obstacles be overcome?" in
Essays on Economic Psychology, Hermann Brandstaetter and Werner Guth, eds. (Berlin, Springer Publishing Company, 1994), pp. 193-212.

Friedrich Schneider, "Further empirical results of the size of the shadow economy of 17 OECD-countries over time", discussion paper to be presented at the fifty-fourth Congress of the International Institute of Public Finance, held in Cordoba, Argentina, in 1998 (Linz, Austria, University of Linz, Department of Economics, 1998).

Tiho Yoo and Jin K. Hyun, "International comparison of the black economy: empirical evidence using micro-level data", unpublished paper presented at the fifty-fourth Congress of the International Institute of Public Finance, held in Córdoba, Argentina, in 1998.

Friedrich Schneider, "The increase of the size of the shadow economy of 18 OECD-countries: some preliminary explanations", paper presented at the Annual Public Choice Meeting, held in Charleston, South Carolina, from 10 to 12 March 2000.

Jan Kloveland, "Tax evasion and the demand for currency in Norway and Sweden: Is there a hidden relationship?",
Scandinavian Journal of Economics, vol. 86, No. 4 (1984), pp. 423-439.

Richard Cebula, "An empirical analysis of the impact of government tax and auditing policies on the size of the underground economy: the case of the United States 1993-1994",
American Journal of Economic Sociology, vol. 56, No. 2 (1997), pp. 173-185.

Roderick Hill and Muhammed Kabir, "Tax rates, the tax mix, and the growth of the underground economy in Canada: What can we infer?"
Canadian Tax Journal/Revue Fiscale Canadienne, vol. 44, No. 6 (1996), pp. 1552-1583.

Friedrich Schneider, Markus F. Hofreither and Reinhard Neck, "The consequences of a changing shadow economy for the official economy: Some empirical results for Austria", in
The Political Economy of Progressive Taxation, Dieter Boes and Bernhard Felderer, eds. (Heidelberg, Springer, 1989), pp. 181-211.

Reinhard Neck, Markus Hofreither and Friedrich Schneider, "The consequences of progressive income taxation for the shadow economy: some theoretical considerations", in
The Political Economy of Progressive Taxation, Dieter Boes and Bernhard Felderer, eds. (Heidelberg, Springer Publishing Company, 1989), pp. 149-176.

A. D. Witte, "The nature and extent of unreported activity: a survey concentrating on recent United States research", in
The Unofficial Economy: Consequences and Perspectives in Different Economic Systems, S. Alessandrini and B. Dallago, eds. (Aldershot, United Kingdom of Great Britain and Northern Ireland, Gower, 1987).

Hans-Georg Petersen, "Size of the public sector, economic growth and the informal economy: development trends in the Federal Republic of Germany",
Review of Income and Wealth, vol. 28, No. 2 (1982), pp. 191-215.

David M. O'Neill, "Growth of the underground economy 1950-81: some evidence from the current population survey", study prepared for the Joint Economic Committee of the United States Congress (Washington, D.C., Government Printing Office, 1983).

Daniela Del Boca and Francesco Forte, "Recent empirical surveys and theoretical interpretations of the parallel economy in Italy", in
The Underground Economy in the United States and Abroad, Vito Tanzi, ed. (Lexington, Massachusetts, Lexington Books, 1982), pp. 160-178.

Daniel Kaufmann and Aleksander Kaliberda, "Integrating the unofficial economy into the dynamics of post-socialist economies: a framework of analyses and evidence", policy research working paper No. 1691 (Washington, D.C., World Bank, 1996).

David Giles, Linsey Tedds and Gugsa Werkneh, "The Canadian underground and measured economies", working paper (Victoria, British Columbia, University of Victoria, Department of Economics, 1999).

Jacques Bendelac and Pierre-Maurice Clair, "Macroeconomic measures of the hidden economy", paper presented at the forty-ninth Congress of the International Institute of Public Finance, held in Berlin in 1993.

4This figure has been derived from polls of the German and Austrian populations about the effects of the shadow economy. For further information, see Schneider [21]. The polls also show that two thirds of the value added accounted for by the shadow economy would not be produced in the official economy if the shadow economy did not exist.

7The physical input (electricity) and the currency demand methods are comparable because both assume an excessive use of a source (electricity and cash, respectively) for shadow-economy activities, and, in both, a "potential GNP" is calculated. The two methods are similarly used by lacko [29-31], Portes [32], Johnson, Kaufmann and Zoido-Lobatón [15, 33], who have applied them to measure a series of shadow economies in a cross section of countries.

8It should be borne in mind that such country comparisons give only a very rough picture of the relative size of the shadow economy in different countries, because each method has its shortcomings. See, for example, Thomas [6, 18], Tanzi [17]. In the comparison presented, the same time periods (either 1989-1990 or 1990-1993) are used for all countries. If possible, the values were calculated as averages for each period.

9The results for the period 1989-1990, which was marked by the collapse of the communist regimes, can only be seen as rough approximations and are therefore not discussed in detail in the present paper.

10The main difference between the two series is that, given a monetary approach, Johnson and others use average values, coming from different sources, of the size of the shadow economy of a country, whereas in Schneider, the currency demand approach and only one value for a given year (or an average over a time period) are used. The problem with using averages from various sources is that: the time period is greater (1985-1995); and the monetary approaches specified by different authors may be quite different.

11Similar rankings are established by Frey and Pommerehne [4], Frey and Weck-Hannemann [39], Williams and Windebank [40], Thomas [6] and Lippert and Walker [9].

12Pioneering work in this area has been done by L. Frey [44-47], Cappiello [48], Lubell [23], Pozo [8], Bartlett [49] and Tanzi [17].

13This is especially true in Europe (for example, in Germany and Austria), where the total tax and social security burden adds up to 100 per cent of the wage effectively earned. See the section below on the increase in the burden of taxation and social security contributions.

16See Schneider [11, 21] for similar findings on the effects of a major tax reform in Austria on the shadow economy. Schneider shows that a major reduction in the direct tax burden did not lead to a major reduction in the shadow economy. Because legal tax avoidance was abolished and other factors, like regulations, were not changed, for many taxpayers the actual tax and regulation burden remained unchanged.

18The higher the top marginal tax rate, the lower the size of the shadow economy.

19Friedman and others [60] found a similar result in a cross-country analysis showing that higher tax rates are associated with less official activity as a percentage of GDP. They argue that entrepreneurs go underground not to avoid official taxes but to reduce the burden of bureaucracy and corruption. However, considering their empirical (regression) results, the finding that higher tax rates are correlated with a lower share of the unofficial economy is not very robust, and in most cases, using different tax rates, they do not find a statistically significant result.

20For a (social) psychological and theoretical foundation of this feature, see Brehm [61, 62], and for a first application to the shadow economy, see Pelzmann [63].

21See, for example, Frey [64] for a first application of the public choice theory to the shadow economy.

28The direct method of voluntary sample surveys has been extensively used for Norway by Isachsen and others [73] and Isachsen and Strom [74]. For Denmark, this method is used by Mogensen and others [25], who report estimates of the shadow economy at 2.7 per cent of GDP for 1989, 4.2 per cent for 1991, 3 per cent for 1993 and 3.1 per cent for 1994.

29The advantages and disadvantages of this method are extensively dealt with by Mogensen and others [25].

30For the United States, see IRS [75, 76], Simon and Witte [77], Witte [78], Clotefelter [79] and Feige [80]. For a more detailed discussion, see Dallago [50] and Thomas [6].

31See, for example, Franz [81], for Austria; MacAfee [82], O'Higgins [83] and Smith [24], for the United Kingdom; Petersen [84] and Del Boca [85], for Germany; and Park [86], for the United States. For a survey and critical remarks, see Thomas [6].

32A related approach is pursued by Pissarides and Weber [87], who use microdata from household budget surveys to estimate the extent of income understatement by the self-employed. In this micro-approach, more or less the same difficulties arise and the figures calculated for the shadow economies may be crude.

33Such studies have been made, for example, by Contini [88] and Del Boca [85], for Italy; and by O'Neill [89], for the United States. For a survey and critical remarks, see Thomas [6].

34For an extended description of this approach, see Feige [5, 90, 91]. For a further application for the Netherlands, see Boeschoten and Fase [92], and for Germany, see Langfeldt [93].

36In table 8 of the present paper, the econometric estimation of such a currency demand function for Austria is shown. More causes of the shadow economy (regulations, different tax rates, complexity of the tax system) are also included. The application of such a currency demand equation has been criticized by Thomas [18], but part of this criticism has been considered by Giles [19-20] and Bhattacharyya [38], who both use the latest econometric techniques.

38One weak justification for the use of only the tax variable is that it has by far the strongest impact on the size of the shadow economy in the studies known to the authors. The only exception is the study by Frey and Weck-Hannemann [39], where the "tax immorality" variable has a quantitatively larger and statistically stronger influence than the direct tax share in the model approach. In the study of the United States by Pommerehne and Schneider [71], which covers various tax measures and provides data on regulations, tax immorality and minimum wage rates, the tax variable has a dominating influence and contributes roughly 60-70 per cent to the size of the shadow economy. See also Zilberfarb [100].

39In another study by Tanzi ([3], pp. 110-113), this criticism is explicitly dealt with. A careful investigation of the amount of United States currency used abroad and in the shadow economy and of traditional criminal activities has been undertaken by Rogoff [104], who concludes that bills of large denomination are the major driving force behind the growth of the shadow economy and traditional criminal activities because of reduced transaction costs.

40However, in studies of European countries, Kirchgaessner [55, 56] and Schneider [26] reach the conclusion that the estimation results for Germany, Denmark, Norway and Sweden are quite robust when using the currency demand method. For Canada, Hill and Kabir find that the rise of the shadow economy varies with respect to the tax variable used and conclude that "when the theoretically best tax rates are selected and a range of plausible velocity values is used, this method estimates underground economic growth between 1964 and 1995 at between 3 and 11 per cent of GDP" ([59], p. 1553).

41This method was used earlier by Lizzeri [105] and Del Boca and Forte [106], and then much later by Portes [32], Kaufmann and Kaliberda [107] and Johnson, Kaufmann and Shleifer [14]. For a critique, see lacko [29-31, 108].

42Johnson, Kaufmann and Shleifer [14] attempt to adjust for changes in the elasticity of electricity/GDP.

43This part is a summarized version from a longer study by Aigner, Schneider and Ghosh ([110], p. 303), applying this approach for the United States over time. The pioneers of this approach are Weck [111] and Frey and Weck-Hannemann [39], who applied this approach to cross-section data from the 24 OECD countries for various years. Before turning to this approach, they developed the concept of "soft modelling" (Frey, Weck and Pommerehne [112] and Frey and Weck [113, 114]), an approach which has been used to provide a ranking of the relative size of the shadow economy in different countries.

44When applying this approach for European countries, Frey and Weck-Hannemann [39] had difficulty in obtaining reliable data for the cause series, besides the ones of direct and indirect tax burden. Hence, their study was criticized by Helberger and Knepel [115], who argue that the results were unstable with respect to changing variables in the model and over the years.